Abstract: A cellular automaton (CA) is a discrete dynamical system composed of an array of cells that only take a finite number of states.
CAs can exhibit complex time evolution patterns and are used as mathematical models for a variety of natural and social phenomena. Ultradiscretization is a mathematical tool for constructing CAs from continuous systems. It has been successfully used to obtain CA models that share important features with continuous phenomena.
The purpose of this organized session is to offer researchers the opportunity to discuss recent advances in ultradiscrete systems and in particular their application to fundamental biology.

MS-Mo-D-10-113:30--14:00Combinatorial and solvable structures of Random Domino AutomatonBialecki, Mariusz (Inst. of Geophysics, Polish Acad. of Sci.)Abstract: We introduce Random Domino Automaton - recently proposed slowly driven system being a stochastic toy model of earthquakes and
also a generalisation of 1D Drossel¨CSchwabl forest-fire model.
A solution of the set of discrete equations describing stationary state of Random Domino Automaton in inverse-power case is presented. We describe also a link to Motzkin numbers.
The presentation emphasizes mathematical structure and properties of the model.

MS-Mo-D-10-214:00--14:30The topology of a DNA string and its gene expressionBao, Yuanyuan (Tohoku Forum for Creativity, Tohoku Univ.)Abstract: Spatial structure and gene expression of a DNA interact with each other in various ways. In this talk, we discuss some topological (structural) properties of a DNA string, regarded as an embedded curve in the 3-space. We then talk about how these properties support the process of gene expression, such as transcription and alternative splicing.

MS-Mo-D-10-314:30--15:00Statistical method for constructing cellular automataKawaharada, Akane (Univ. of Shizuoka)Abstract: We propose a statistical construction method of cellular automata based on observation data.
Cellular automaton are discrete dynamical systems whose configurations are determined
by local rules acting on each cell in synchronous.
Since cellular automata generate rich and complex behaviors,
we can expect they are good models for simulating phenomena.
In this talk, we introduce the method and apply to some physical phenomena.
Cellular automata with three neighbors and 2¨C8 states are obtained.

MS-Mo-D-10-415:00--15:30Modeling cell-cell interactions in gliomasBadoual, Mathilde (Paris Diderot Univ.)Abstract: Diffuse low-grade gliomas are brain tumors that grow slowly, but that are incurable because some glioma cells migrate within the parenchyma surrounding the tumor.
Here, we will present a stochastic approach, based on a cellular automaton, where the interactions between migrating cells are taken into account and the properties of the correlations between cells are studied in order to characterise the leading edge of the tumor. We also calculated the continuous limit.